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Convexity properties of information functionals for Gaussian mixtures

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If you have a question about this talk, please contact Dr Varun Jog .

We consider the entropy and Fisher information of Gaussian mixtures, that is centered Gaussians with randomly chosen variance. For the entropy, we will show that a concavity conjecture of Ball, Nayar and Tkocz (2016) holds true for this class of random variables. For the Fisher information, we will first present a simple upper bound. In order to extend this bound to higher dimensions, we will show that the Fisher information matrix is in general operator convex as a matrix-valued functional of the density, extending a result of Bobkov (2022). Finally, as an application, we will discuss convergence rates for the Fisher information of weighted sums of Gaussian mixtures in the CLT .

This is joint work with Alexandros Eskenazis (Sorbonne and Cambridge).

This talk is part of the Information Theory Seminar series.

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